FIG. 1 illustrates a prior art implementation 10 of a tuner-filter-decimator which is a conventional technique for separating a complex input signal into upper sideband and lower sideband complex signals.
The complex digitally sampled signal of interest (SOI) to be processed (referred to as xk) has an input bandwidth at a sample rate of Fs of, e.g., −Fs/4 to +Fs/4. One half of the samples are processed by an upper sideband (USB) portion of the processing circuitry (see, e.g., the upper portion of the circuit illustrated in FIG. 1) and the other half of the samples are processed by a lower sideband (LSB) portion of the processing circuitry (see, e.g., the lower portion of the circuit illustrated in FIG. 1). In FIG. 1, a USB tuner formed by multiplier 12 tunes the input signal xk on line 14 down by frequency −Fs/8 by multiplying input signal xk on line 14 by the sequence Sk=e−j2πk/8 for k=0, 1, 2, 3, . . . to generate a complex signal on line 18 centered on an upper sideband center frequency. In a similar manner, an LSB tuner formed by multiplier 20 tunes the input signal xk on line 14 up by frequency +Fs/8 by multiplying input signal xk on line 14 by the sequence S′k=e+j2πk/8 for k=0, 1, 2, 3, . . . on line 22 to generate a complex signal on line 24 centered on the lower sideband center frequency. A low pass Finite Impulse Response (FIR) filter 26 (in this case of length 13) filters the USB signal on line 18 and produces a filtered USB signal on line 28 which has been sufficiently filtered of the LSB signal and other out-of-band signal components to support the decimation process that follows. Similarly, a low pass FIR filter 30 (also of length 13 in this example) filters the LSB signal on line 24 and produces a filtered LSB signal on line 32 which has been sufficiently filtered of the USB signal and other out-of-band signal components to support the decimation process that follows. A decimator 34 accepts the filtered USB signal on line 28 and discards every other sample, thereby decimating the signal by a factor of 2 to produce tuned, filtered and decimated USB complex signal yuk on line 36. Likewise, a decimator 38 accepts the filtered LSB signal on line 32 and discards every other sample, thereby decimating the signal by a factor of 2 to produce tuned, filtered and decimated USB complex signal ylk on line 40.
The implementation of the prior art digital tuner-filter-decimator in FIG. 1 requires 26 memory storage registers and 26 multipliers to implement the two length 13 low pass FIR filters 26, 30. Further increasing the complexity of the implementation, the tuner-filter-decimator 10 of FIG. 1 requires complicated multipliers 12, 20 for the tuners that are each capable of multiplying by non-trivial values such as √{square root over (2)}(=1.4142135 . . . ) rather than trivial values such as +1 and −1. A simpler implementation would be desirable, particular for use with multi-channel receivers.